SRC/dsgesv.f(3)

💅 SRC/dsgesv.f(3) — Library Functions Manual ✨

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💖 NAME 💖

SRC/dsgesv.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

• subroutine dsgesv (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, iter, info) — DSGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

subroutine dsgesv (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork,
    iter, info)

🌸 Function/Subroutine Documentation 🌸

subroutine dsgesv (integer n, integer nrhs, double precision, dimension(
    lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, *
    ) x, integer ldx, double precision, dimension( n, * ) work, real,
    dimension( * ) swork, integer iter, integer info)

DSGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

🎯 Purpose

okay so DSGESV computes the solution to a real system of linear equations

A * X = B,

where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

DSGESV first attempts to factorize the matrix in SINGLE PRECISION and use this factorization within an iterative refinement procedure to produce a solution with DOUBLE PRECISION normwise backward error quality (see below). If the approach fails the method switches to a DOUBLE PRECISION factorization and solve.

ngl, the iterative refinement is not going to be a winning strategy if the ratio SINGLE PRECISION performance over DOUBLE PRECISION performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement.

The iterative refinement process is stopped if

ITER > ITERMAX

or for all the RHS we have:

RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX

where

• ITER is the number of the current iteration in the iterative refinement process
• RNRM is the infinity-norm of the residual
• XNRM is the infinity-norm of the solution
• ANRM is the infinity-operator-norm of the matrix A
• EPS is the machine epsilon returned by DLAMCH('Epsilon')

The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.

🧾 Parameters

• N — N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the N-by-N coefficient matrix A. On exit, if iterative refinement has been successfully used (INFO = 0 and ITER >= 0, see description below), then A is unchanged; if double precision factorization has been used (INFO = 0 and ITER < 0, see description below), then the array A contains the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
• LDA — LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N) The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i). Corresponds either to the single precision factorization (if INFO = 0 and ITER >= 0) or the double precision factorization (if INFO = 0 and ITER < 0).
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS) The N-by-NRHS right hand side matrix B.
• LDB — LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS) If INFO = 0, the N-by-NRHS solution matrix X.
• LDX — LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
• WORK — WORK is DOUBLE PRECISION array, dimension (N,NRHS) This array is used to hold the residual vectors.
• SWORK — SWORK is REAL array, dimension (N*(N+NRHS)) This array is used to use the single precision matrix and the right-hand sides or solutions in single precision.
• ITER — ITER is INTEGER
  • < 0: iterative refinement has failed, double precision factorization has been performed
    • -1: the routine fell back to full precision for implementation- or machine-specific reasons
    • -2: narrowing the precision induced an overflow, the routine fell back to full precision
    • -3: failure of SGETRF
    • -31: stop the iterative refinement after the 30th iterations
  • > 0: iterative refinement has been successfully used. Returns the number of iterations
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, U(i,i) computed in DOUBLE PRECISION is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.

👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 193 of file dsgesv.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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